2x(3+3x)=18(14)

Solution for 2x(3+3x)=18(14) equation:

2x(3+3x)=18(14)

We move all terms to the left:

2x(3+3x)-(18(14))=0

determiningTheFunctionDomain
2x(3+3x)-1814=0

We add all the numbers together, and all the variables

2x(3x+3)-1814=0

We multiply parentheses

6x^2+6x-1814=0

a = 6; b = 6; c = -1814;
Δ = b2-4ac
Δ = 62-4·6·(-1814)
Δ = 43572
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{43572}=\sqrt{4*10893}=\sqrt{4}*\sqrt{10893}=2\sqrt{10893}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{10893}}{2*6}=\frac{-6-2\sqrt{10893}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{10893}}{2*6}=\frac{-6+2\sqrt{10893}}{12}
$